Question

A school administrator is concerned about the amount of credit-card debt that college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have credit-card debt of $2000 or more. What size sample should be obtained if she wishes the estimate to be within 2 percentage points with 90% confidence if...

a) no prior estimate is available?   n=

b) a pilot study indicates that the percentage is 28%? n=

Answer 1

Solution :

Given that,

a)

= 1 - = 0.5

margin of error = E = 0.02

Z/2 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.02)2 * 0.5 * 0.5

= 1691

sample size = n = 1691

b)

= 0.28

1 - = 1 - 0.28 = 0.72

margin of error = E = 0.02

Z/2 = 1.645

sample size = n = (Z / 2 / E )2 * * (1 - )

= (1.645 / 0.02)2 * 0.28 * 0.72

= 1364

sample size = n = 1364